How Do You Solve a Calculus Limit Involving Negative Infinity?

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Homework Help Overview

The discussion revolves around evaluating a limit involving the expression \(\frac{\sqrt{x^2 - 3x}}{2x + 1}\) as \(x\) approaches negative infinity. Participants are exploring the implications of the negative infinity aspect in the context of calculus.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants express confusion about handling the limit as \(x\) approaches negative infinity, with some attempting to substitute values or manipulate the expression. There are suggestions to use the absolute value and to multiply by the conjugate as potential strategies.

Discussion Status

There is an ongoing exploration of different approaches, with some participants offering guidance on techniques to consider. However, there is no explicit consensus on a single method to solve the limit, and multiple interpretations of the problem are being discussed.

Contextual Notes

Some participants mention the rules of the forum and the importance of adhering to them, indicating a focus on collaborative learning rather than direct solutions.

darklordavion
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Homework Statement



Limit: The square root of X^2-3X over 2X+1 as X is going towards negative infinity.



Homework Equations



The square root of X^2-3X over 2X+1 as X is going towards negative infinity.

The Attempt at a Solution



I tried to solve it but I have no idea what to do with the negative infinity part. I mean, if it was one number, I would just sub in that number and maybe factor, I am totally lost!
 
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darklordavion said:

Homework Statement



Limit: The square root of X^2-3X over 2X+1 as X is going towards negative infinity.



Homework Equations



The square root of X^2-3X over 2X+1 as X is going towards negative infinity.

The Attempt at a Solution



I tried to solve it but I have no idea what to do with the negative infinity part. I mean, if it was one number, I would just sub in that number and maybe factor, I am totally lost!

[tex]\sqrt{x^2 - 3x} = |x|\sqrt{1 - 3/x}[/tex]
Does that help?
 
This: √X^2-3X
lim x→-∞ _________
Divided by 2X+1 Like that ^
 
Yes, I understand what the problem is. I was suggesting something that might help you with it.
 
WHy can't you use L'Hospital's rule?
 
Mark44 said:
Yes, I understand what the problem is. I was suggesting something that might help you with it.

Oh sorry :( lol, I thought you interpreted it wrong.

I've tried just subing a random number, which was 4 and got 2/9... not sure what to do next.
 
multiply by the conjugate

it is like multiplying by 1, which is not ilegal, but it will cancel out things to you and make life easier
 
stonecoldgen said:
multiply by the conjugate

it is like multiplying by 1, which is not ilegal, but it will cancel out things to you and make life easier

can you show me?
 
Never mind, a friend who took BC cal last year helped me through AIM.

I got it :) Less work than needed too :)
 
  • #10
darklordavion said:
can you show me?
We are not here to do your work for you. Several people have suggested things to try. Pick one of the techniques and see what you get.

If you haven't taken a close look at the rules of Physics Forums (which you agreed to abide by when you joined it), you can find them here: https://www.physicsforums.com/showthread.php?t=414380

The section on Homework Help is applicable here.
 

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